Portages and routes were often indicated by lob trees, or trees that had their branches cut off just below the top of the tree.
32.
Branch cuts allow one to work with a collection of single-valued functions, " glued " together along the branch cut instead of a multivalued function.
33.
Single-valued, one makes a branch cut along the interval [ 0, 1 ] on the real axis, connecting the two branch points of the function.
34.
The branch cut device may appear arbitrary ( and it is ); but it is very useful, for example in the theory of special functions.
35.
What have I done wrong, because I can't see how my answers would change if we took a different branch cut-are the answers even correct?
36.
Branch cuts allow one to work with a collection of single-valued functions, " glued " together along the branch cut instead of a multivalued function.
37.
Therefore, these formulas define convenient principal values, for which the branch cuts are and for the inverse hyperbolic tangent, and for the inverse hyperbolic cotangent.
38.
The sum converges for all complex z, and we take the usual value of the complex logarithm having a branch cut along the negative real axis.
39.
The fact that the whole branch cuts appear as discontinuities, shows that these principal values may not be extended into analytic functions defined over larger domains.
40.
A similar problem appears with other complex functions with branch cuts, e . g ., the complex logarithm and the relations or which are not true in general.
